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18 Aug 2003, 05:55
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Q. At how many points does the line y = ax^2 + 2qx + r cut the X-axis.
1) q> r^2
2) 2r > q^2
I do not have the official answer, but hope you can solve this
1) q> r^2
2) 2r > q^2
I do not have the official answer, but hope you can solve this
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18 Aug 2003, 07:22
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are you sure that everything is correct in the statement?
component ax^2 indicates that this is not a line, it's a parabola.
what is the source of question?
anyway, the Line always crosses and axis in one point
component ax^2 indicates that this is not a line, it's a parabola.
what is the source of question?
anyway, the Line always crosses and axis in one point
18 Aug 2003, 07:44
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MBA04
Q. At how many points does the line y = ax^2 + 2qx + r cut the X-axis.
1) q> r^2
2) 2r > q^2
I do not have the official answer, but hope you can solve this
1) q> r^2
2) 2r > q^2
I do not have the official answer, but hope you can solve this
Answer is E
For any quadratic ax^2+bx+c,
if b^2-4ac >0, then the equation has two real roots (i.e. it cuts the x axis in two distinct points)
if b^2-4ac = 0, then the equation has two real roots that are equal (i.e. it cuts in one distinct point)
if b^2-4ac < 0 then the equation does not have any real roots
Now condition (1) tells us that q>r^2. But this does not tell us whether 4q^2-4ar is >0, =0 or <0 since the value of a in unknown
Condition (2) tells us that 2r>q^2. Again, the value of a is unknown so we cannot arrive at a clear answer to the question.
Together also they do not help.
Hence E
